Question: Which of these numbers is prime? ${23,\ 35,\ 65,\ 78,\ 81}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 23 are 1 and 23. The factors of 35 are 1, 5, 7, and 35. The factors of 65 are 1, 5, 13, and 65. The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. The factors of 81 are 1, 3, 9, 27, and 81. Thus, 23 is a prime number.